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Risk and uncertainty are crucial factors in decision-making processes, especially when integrating emerging technologies into essential systems like supply chains. Failing to adequately consider significant risks can disrupt supply chain operations, leading to a loss of competitive edge and causing financial and reputational damage. On the other hand, the complex nature of new technology environments, differing viewpoints among stakeholders, and the challenges of interpreting data introduce a variety of uncertainties in decision-making. In this study, we conduct a thorough examination of how blockchain strategies can be applied within supply chain frameworks. Our analysis utilizes data-driven network decision-making models that are refined to effectively manage uncertainty and risk. These models take into account aspects such as supply chain dynamics and technological factors. Importantly, we meld risk considerations with our models to tackle efficiency shortfalls, while also accounting for uncertainty caused by ambiguous and stochastic data environments. By applying and assessing these models in a real-world case study of the oil and gas industry, our research uncovers insightful observations. Specifically, we find that adopting a localization strategy presents specific risks, while a single-use strategy yields significant efficiency improvements.

The recent adoption of modern technologies has led to the fourth industrial revolution or Industry 4.0 (I4.0). The supply chain of large industries, such as steel, is of significant importance in the economies of countries. According to data published by the National Iranian Steel Company, the steel industry is one of the most vital sectors in Iran, contributing about 1 % to its Gross Domestic Product (GDP). Therefore, implementing I4.0 in the steel supply chain is a highly significant and practical endeavor, with the potential to drive considerable advancements in this industry. This study develops an efficient integrated framework to identify and evaluate the most critical factors influencing the implementation of I4.0 in the supply chains of large industries. The study also reviews the most effective policies for implementing these factors and analyzes the gap between the current state of the steel supply chain in Iran and the desired state within the framework of I4.0. The components of I4.0 are determined based on a review of existing literature and interviews with experts from the Iranian steel industry, utilizing the fuzzy Delphi method. Afterward, Strengths, Weaknesses, Opportunities, and Threats (SWOT) policies are developed. The optimal combination of policies for implementing I4.0 in the Iranian steel supply chain is identified using game theory. Finally, a gap analysis is conducted between the current state of the industry and the desired state. The critical gap analysis revealed that the current state of the supply chain significantly lags behind the desired I4.0 goals, particularly in terms of infrastructure and supply chain balancing. The findings highlight a stark contrast between the current performance score of 0.16 and the target score of 0.84, underscoring the substantial improvements needed to realize I4.0 within this sector.

Purpose: The COVID-19 pandemic has led to a significant crisis in society's health, industries, and businesses. In this regard, the medical devices industry has played an important role in crisis management and providing healthcare and has faced several major challenges in supplying raw materials, production activities, and distribution activities due to the disruptions caused by the pandemic. One of the critically important issues in the medical devices supply chain is supplier selection. Hence, this research investigates the supplier selection problem considering the emerging concepts that have dramatically attracted the attention of researchers after the COVID-19 pandemic, namely viability and Industry 5.0.Methodology: In this study, a hybrid fuzzy decision-making approach is developed to investigate the viable supplier selection problem considering the Industry 5.0 dimensions. In this regard, in the first stage, according to the literature and experts, the main indicators of the research problem are extracted, and their weights are calculated using the fuzzy best-worst method. In the next stage, the feasible suppliers are evaluated by employing the fuzzy VIKOR method. Also, to show the robustness and validation of the proposed approach, its results are compared with those of traditional approaches.Findings: In this study, a list of indicators, including six aspects and 34 criteria, is provided for the research problem based on its nature, and their importance has been computed. Based on the outputs, the general metric is the most important aspect, and the human-centricity metric is the least significant. Also, the results show that in addition to the general criteria, such as cost and quality, other criteria, such as reliability, technical capability, pollution control, risk reduction, and service, also play a significant role in the process of selecting suppliers. The results indicate that managers in today's competitive and industrial markets should redirect their attention from traditional criteria to those contributing to the sustainability and improvement of their systems' performance.Originality/Value: Reading the results of this research can help Industrial and organizational managers evaluate the potential suppliers of their companies based on the viability and Industry 5.0 dimensions and select the best ones, which can significantly improve the performance and efficiency of their businesses.

Plant diseases threaten agricultural sustainability by reducing crop yields. Rapid and accurate disease identification is crucial for effective management. Recent advancements in artificial intelligence (AI) have facilitated the development of automated systems for disease detection. This study focuses on enhancing the classification of diseases and estimating their severity in coffee leaf images. To do so, we propose a novel approach as the preprocessing step for the classification in which enhanced multivariance product representation (EMPR) is used to decompose the considered image into components, a new image is constructed using some of those components, and the contrast of the new image is enhanced by applying high-dimensional model representation (HDMR) to highlight the diseased parts of the leaves. Popular convolutional neural network (CNN) architectures, including AlexNet, VGG16, and ResNet50, are evaluated. Results show that VGG16 achieves the highest classification accuracy of approximately 96%, while all models perform well in predicting disease severity levels, with accuracies exceeding 85%. Notably, the ResNet50 model achieves accuracy levels surpassing 90%. This research contributes to the advancement of automated crop health management systems.

The optimization of sustainable smart cities is an essential endeavor in modern urban development, aiming to enhance the quality of life for citizens while minimizing environmental impacts. Big data plays a critical role in achieving these goals by enabling the collection, analysis, and utilization of vast amounts of information to make informed decisions. However, implementing big data in smart cities faces significant barriers, including data-sharing challenges, technical limitations, and organizational non-cooperation. Addressing these barriers is crucial for the successful deployment of smart city initiatives. We propose a novel approach to tackle these challenges using the Improved Zero-Sum Grey Game (IZSGG) theory and the Grey Best-Worst Method (G-BWM). This method comprehensively analyzes the risks and uncertainties associated with big data implementation in smart cities. By modeling the interactions between different stakeholders and their competing interests, IZSGG theory provides a framework to identify optimal strategies for data management. The G-BWM further refines these strategies by evaluating and prioritizing the various factors influencing big data utilization. Our findings reveal that the worst-case scenario for a smart city involves the simultaneous occurrence of several risks, all of which have positive values, indicating their potential to significantly disrupt smart city operations. The specific risks identified include: the sharing of data and information, the collection and recording of data, technical limitations and challenges associated with technology, the non-cooperation of organizations, and issues related to the interpretation of complex information. The technical barrier is the most significant with a weight of w(T)=0.6152, indicating its critical role compared to other barriers. Within this category, the sub-barrier of technical and technological constraints is particularly critical, with a weight of 0.39267375.

Sustainability means the most effective and efficient use of existing resources to meet the needs of future and current generations. Nowadays, with the increase in global environmental problems as well as social and economic problems, sustainability in the supply chain of the automotive industry has become increasingly important. In our study, after conducting an extensive literature review in the automotive industry, consulting with experts, and identifying 35 different Sustainability Risks across 5 sustainability dimensions, we proposed a total of 40 risk strategies to mitigate these risks. Using the evaluations of automotive supply chain experts from one of Turkey's leading logistics companies, risk strategies were ranked using the Interval-Valued Neutrosophic Fuzzy Evaluation based on Distance from Average Solution (IVN Fuzzy EDAS) method, and the best strategies were determined. Accordingly, it has been determined that the optimal approach for companies is to establish and implement legal compliance procedures and programs while adhering to prevailing regulations and policies. It aims to make a useful contribution to the literature in terms of covering this subject for the first time with fuzzy EDAS method, adding new sustainability risk dimensions, and developing broad-level risk and risk prevention strategies on the subject. In this study, the interval-valued neutrosophic fuzzy EDAS method was applied for the first time to the issue of sustainability risks in the automotive industry. At the same time, this study aims to contribute to the literature by adding new dimensions to sustainability.

The global impact of the COVID-19 pandemic, characterized by its extensive societal, economic, and environmental challenges, escalated with the emergence of variants of concern (VOCs) in 2020. Governments, grappling with the unpredictable evolution of VOCs, faced the need for agile decision support systems to safeguard nations effectively. This article introduces the Variant-Informed Decision Support System (VIDSS), designed to dynamically adapt to each variant of concern’s unique characteristics. Utilizing multi-attribute decision-making (MADM) techniques, VIDSS assesses a country’s performance by considering improvements relative to its past state and comparing it with others. The study incorporates transfer learning, leveraging insights from forecast models of previous VOCs to enhance predictions for future variants. This proactive approach harnesses historical data, contributing to more accurate forecasting amid evolving COVID-19 challenges. Results reveal that the VIDSS framework, through rigorous K-fold cross-validation, achieves robust predictive accuracy, with neural network models significantly benefiting from transfer learning. The proposed hybrid MADM approach integrated approaches yield insightful scores for each country, highlighting positive and negative criteria influencing COVID-19 spread. Additionally, feature importance, illustrated through SHAP plots, varies across variants, underscoring the evolving nature of the pandemic. Notably, vaccination rates, intensive care unit (ICU) patient numbers, and weekly hospital admissions consistently emerge as critical features, guiding effective pandemic responses. These findings demonstrate that leveraging past VOC data significantly improves future variant predictions, offering valuable insights for policymakers to optimize strategies and allocate resources effectively. VIDSS thus stands as a pivotal tool in navigating the complexities of COVID-19, providing dynamic, data-driven decision support in a continually evolving landscape.

The widely recognized measure for resources called resource strength (RS) does not fully capture the resources complexity of a project. Therefore, it cannot be used as a standalone measure to distinguish the complexity of various instances of project scheduling problems. Consequently, additional resource measures such as total amount of overflow (TAO) have been introduced, which should be used in conjunction with the RS. Extensive experimental studies have shown that as the value of TAO increases in a project, scheduling schemes with higher dimensional scheduling schemes such as bi-directional and tri-directional result in schedules with shorter makespans. In this study, an effective approach is proposed for integrating projects in multi-project environments, called the integrated project approach (IPA), taking into account the influence of TAO and building upon the relation between the TAO and the scheduling generation schemes. To assess the performance of IPA, we develop a new random multi-project generator based on the well-known benchmark sets, which utilizes TAO as a control tool to generate instances. The findings indicate that prioritizing the projects and frequency of the projects integration, facilitated by the proposed IPA, have a positive impact on the quality of multi-project schedules.

Waste management involves the systematic collection, transportation, processing, and treatment of waste materials generated by human activities. It entails a variety of strategies and technologies to diminish environmental impacts, protect public health, and conserve resources. Consequently, providing an effective and comprehensive optimization approach plays a critical role in minimizing waste generation, maximizing recycling and reuse, and safely disposing of waste. This work develops a novel Possibilistic Multi-Objective Mixed-Integer Linear Programming (PMOMILP) model in order to formulate the problem and design a circular–sustainable–reliable waste management network, under uncertainty. The possibility of recycling and recovery are considered across incineration and disposal processes to address the main circular-economy principles. The objectives are to address sustainable development throughout minimizing the total cost, minimizing the environmental impact, and maximizing the reliability of the Waste Management System (WMS). The Lp-metric technique is then implemented into the model to tackle the multi-objectiveness. Several benchmarks are adapted from the literature in order to validate the efficacy of the proposed methodology, and are treated by CPLEX solver/GAMS software in less than 174.70 s, on average. Moreover, a set of sensitivity analyses is performed to appraise different scenarios and explore utilitarian managerial implications and decision aids. It is demonstrated that the configured WMS network is highly sensitive to the specific time period wherein the WMS does not fail.

Early identification of false news is now essential to save lives from the dangers posed by its spread. People keep sharing false information even after it has been debunked. Those responsible for spreading misleading information in the first place should face the consequences, not the victims of their actions. Understanding how misinformation travels and how to stop it is an absolute need for society and government. Consequently, the necessity to identify false news from genuine stories has emerged with the rise of these social media platforms. One of the tough issues of conventional methodologies is identifying false news. In recent years, neural network models’ performance has surpassed that of classic machine learning approaches because of their superior feature extraction. This research presents Deep learning-based Fake News Detection (DeepFND). This technique has Visual Geometry Group 19 (VGG-19) and Bidirectional Long Short Term Memory (Bi-LSTM) ensemble models for identifying misinformation spread through social media. This system uses an ensemble deep learning (DL) strategy to extract characteristics from the article’s text and photos. The joint feature extractor and the attention modules are used with an ensemble approach, including pre-training and fine-tuning phases. In this article, we utilized a unique customized loss function. In this research, we look at methods for detecting bogus news on the internet without human intervention. We used the Weibo, liar, PHEME, fake and real news, and Buzzfeed datasets to analyze fake and real news. Multiple methods for identifying fake news are compared and contrasted. Precision procedures have been used to calculate the proposed model’s output. The model’s 99.88% accuracy is better than expected.

Generalized Vehicle Routing Problem (GVRP) is a challenging operational research problem which has been widely studied for nearly two decades. In this problem, it is assumed that graph nodes are grouped into a number of clusters, and serving any node of a cluster eliminates the need to visit the other nodes of that cluster. The general objective of this problem is to find the set of nodes to visit and determine the service sequence to minimize the total traveling cost. In addition to these general conditions, GVRP can be formulated with different assumptions and constraints to practically create different sub-types and variants. This paper aims to provide a comprehensive survey of the GVRP literature and explore its various dimensions. It first encompasses the definition of GVRP, similar problems, mathematical models, classification of different variants and solution methods developed for GVRPs, and practical implications. Finally, some useful suggestions are discussed to extend the problem. For this review study, Google Scholar, Scopus, Science Direct, Emerald, Springer, and Elsevier databases were searched for keywords, and 160 potential articles were extracted, and eventually, 45 articles were judged to be relevant.

Abstract With the development of communication infrastructure, the design of supply chains has changed significantly. Blockchain technology, as one of the most cutting-edge technologies, can promote transparency among members of the supply chain network. To the best of our knowledge, this is the first study that tries to develop a novel bi-objective optimization model to integrate the transparency resulting from the use of blockchain for designing a three-level supply chain network. The first objective function is to minimize total cost while the second objective function seeks to maximize transparency based on the application of blockchain technology. Moreover, it is worth noting that it is the first attempt to investigate the role of a blockchain model under stochastic conditions. The bi-objectiveness and stochastic nature of the proposed model are then treated using Fuzzy Goal Programming (FGP) and Chance-Constrained programming (CCP) approaches, respectively. To tackle the problem, an improved Branch and Efficiency (B&E) algorithm is developed by incorporating transparency along with cost and service. The impacts of blockchain exclusively through transparency (Case 1) or through transparency, cost, and benefits (Case 2) in Supply Chain Design (SCD) are compared. The results demonstrated that the first case has less computational complexity and better scalability, while the second case has more transparency, less congestion, and more security. As one of the main implications, supply chain managers who are focused on cost minimization as well as transparency maximization are advised to take into account the trade-off between featuring costs and benefits of blockchain technology.

The process of software development is incomplete without software testing. Software testing expenses account for almost half of all development expenses. The automation of the testing process is seen to be a technique for reducing the cost of software testing. An NP-complete optimization challenge is to generate the test data with the highest branch coverage in the shortest time. The primary goal of this research is to provide test data that covers all branches of a software unit. Increasing the convergence speed, the success rate, and the stability of the outcomes are other goals of this study. An efficient bioinspired technique is suggested in this study to automatically generate test data utilizing the discretized Bat Optimization Algorithm (BOA). Modifying and discretizing the BOA and adapting it to the test generation problem are the main contributions of this study. In the first stage of the proposed method, the source code of the input program is statistically analyzed to identify the branches and their predicates. Then, the developed discretized BOA iteratively generates effective test data. The fitness function was developed based on the program’s branch coverage. The proposed method was implemented along with the previous one. The experiments’ results indicated that the suggested method could generate test data with about 99.95% branch coverage with a limited amount of time (16 times lower than the time of similar algorithms); its success rate was 99.85% and the average number of required iterations to cover all branches is 4.70. Higher coverage, higher speed, and higher stability make the proposed method suitable as an efficient test generation method for real-world large software.

Although the construction industry, especially because of its relationship with other economic sectors, is one of the most important sectors that plays a key role in a country's economic growth, the construction supply chain has been considered less attention. Therefore, construction supply chain network design is of great importance for not only the companies but also governments. Thus, presenting an original mixed integer linear programming model, this paper introduces an optimal framework for a multi-project multi-resource multi-supplier construction supply chain network design for large construction companies with a decentralized procurement strategy. The main objective is to design a reliable supply chain model based on the quality of projects under the certain predefined budget, considering the entire supply chain as a single entity. Using a bi-objective approach to formulate the chain and the Lp-metric approach to solve the problem, make it possible to obtain a single-objective structural framework to reliability-quality trade-off consideration. To solve the problem in small and medium scales, GAMS software is employed, and a hybrid algorithm based on Genetic Algorithm (GA) and Simulated Annealing (SA) algorithm is developed to solve the large-scaled problem. The results show the capability of the model to attain optimal size of the chain as well as the quality-reliability trade-off considering a pre-specified budget. And, to the best of authors knowledge this is the first to obtain such a structured integrated framework in the construction supply chain.

Nowadays, the business landscape is highly focused on establishing efficient logistics systems, with numerous companies striving to gain a strong foothold in the global market and achieve maximum productivity and cost effectiveness [...]

The integration of big data analytics and cognitive computing results in a new model that can provide the utilization of the most complicated advances in industry and its relevant decision-making processes as well as resolving failures faced during big data analytics. In E-projects portfolio selection (EPPS) problem, big data-driven decision-making has a great importance in web development environments. EPPS problem deals with choosing a set of the best investment projects on social media such that maximum return with minimum risk is achieved. To optimize the EPPS problem on social media, this study aims to develop a hybrid fuzzy multi-objective optimization algorithm, named as NSGA-III-MOIWO encompassing the non-dominated sorting genetic algorithm III (NSGA-III) and multi-objective invasive weed optimization (MOIWO) algorithms. The objectives are to simultaneously minimize variance, skewness and kurtosis as the risk measures and maximize the total expected return. To evaluate the performance of the proposed hybrid algorithm, the data derived from 125 active E-projects in an Iranian web development company are analyzed and employed over the period 2014-2018. Finally, the obtained experimental results provide the optimal policy based on the main limitations of the system and it is demonstrated that the NSGA-III-MOIWO outperforms the NSGA-III and MOIWO in finding efficient investment boundaries in EPPS problems. Finally, an efficient statistical-comparative analysis is performed to test the performance of NSGA-III-MOIWO against some well-known multi-objective algorithms.

One of the most important issues of concern to human societies in recent years is urban waste management that is one of the main requirements of each city, and without any notice of it, it can be problematic for it and even residents of the surrounding villages. Urban areas generate the highest amount of waste and consequently, they need an efficient system for collecting and disposing of waste where its determination and stabilization is very difficult and costly. In this regard, this paper examines the multi-trip vehicle routing problem with time windows specific to the urban waste collection, with the goal is to minimize the total cost including routing costs, the earliness and lateness penalty cost for violating the service time windows and the usage costs of vehicles. To solve the problem in practical dimensions, grey wolf optimization (GWO) algorithm is developed where its performance is tested compared to CPLEX solver of GAMS and simulated annealing (SA) algorithm. The obtained results demonstrate that the proposed GWO have an acceptable performance to generate high-quality solutions. Finally, to study the behavior of the objective function versus the real-world demand parameter changes, a sensitivity analysis is performed on this parameter and the optimal management policy is analyzed.ed.

Scheduling is known as a great part of production planning in manufacturing systems. Flow Shop Scheduling (FSS) problem deals with the determination of the optimal sequence of jobs processing on machines in a fixed order. This paper addresses a novel robust FSS problem with outsourcing option where jobs can be either scheduled for inside or outsourced to one of the available subcontractors. Capacity limitation for inside resource, just-in-time delivery policy and uncertain processing time are the key assumptions of the proposed model. The objective is to minimize the total-weighted time required to complete all jobs and the total cost of outsourcing. So, a Robust Mixed-Integer Linear Programming (RMILP) model is proposed to accommodate the problem with the real-world conditions. Finally, the obtained results show the effects of the robustness in optimizing the model under uncertainty condition. Moreover, the comparison analysis demonstrated the superiority of our proposed model against the previous Non-Linear Programming (NLP) model in the literature.

Athletes, both professional and amateur, are always looking for ways to improve their performance. With the introduction and increasing availability of modern technologies and smart devices arose the need to measure and analyze performance, but likewise, the use of these innovations as a competitive advantage also arose. Scientific publications reflect the wide range of available approaches and technologies, as well as the growing interest in various sports. As a result, we concentrated on a systematic review of publications that presented performance analysis tools and methods in all sports, with a final focus on racket sports. Clarivate Analytics’ Web of Science (WoS) and Elsevier Inc.’s SCOPUS databases were searched for 1147 studies that conducted performance analysis and sports research and were published in English. The data in the systematic review are current, up until 18 May 2021. A general review was performed on 759 items, and then 65 racket sports publications were thoroughly scrutinized. We concentrated on performance data, data collection and analysis tools, performance analysis methods, and software. We also talked about performance prediction. In performance research, we have identified specific approaches for specific sports as well as key countries. We are also considering expanding performance analysis in to E-sports in the future.

Iran is among the ten disaster-prone countries and, in terms of the earthquake, it has been ranked the sixth in the world. Although the damages caused by the disasters are not irreversible from different aspects, they could be minimized by performing appropriate preventions as well as preparing plans to counteract the impacts of such incidents. According to the increasing trend of disasters and crises, which hardly damage businesses and communities, providing relief supply chain for crisis situations (HDRSC) is necessary and vital in the wide field of supply chain management (SCM). Even though considerable attempts have been performed in the field of supply chain focusing on the disaster relief, few studies have addressed its complex features and properties. This paper concentrates on the activities such as demand determination and supply chain coordination by field study and best review of best-related research. This research provides a framework for supply chain managers in crisis, who face similar problems in other environments, with valuable insights.

Due to the complexity of real-world multi-criteria decision-making (MCDM) issues, analyzing different opinions from a group of decision makers needs to ensure appropriate decision making. The group decision-making methods collect preferences of the decision makers and present the best preferences using mathematical equations. The best–worst method (BWM) is one of the recently introduced MCDM methods that requires fewer pairwise comparisons to obtain the criteria weights than the other MCDM methods. In this research, we develop a novel approach to group decision-making problems based on the BWM called G-BWM. This approach helps us to analyze the preferences of decision makers to carry out democratic decision making using the BWM structure. In order to assess the applicability of the proposed methodology and represent its novelty, two numerical examples from the literature with the application to supply chain management (SCM) (i.e., green supplier selection and supplier development/segmentation) are examined and discussed. The results demonstrate the performance of our proposed G-BWM for group decision making in terms of a large number of decision makers, ease of use and achieving democratic decisions in the decision-making process.

Along with the increased competition in production and service areas, many organizations attempt to provide their products at a lower price and higher quality. On the other hand, consideration of environmental criteria in the conventional supplier selection methodologies is required for companies trying to promote green supply chain management (GSCM). In this regard, a multi-criteria decision-making (MCDM) technique based on analytic hierarchy process (AHP) and fuzzy technique for order of preference by similarity to ideal solution (TOPSIS) is used to evaluate and rate the suppliers. Then, considering the resource constraint, weight of criteria and a rank of suppliers are taken into account in a multi-objective mixed-integer linear programming (MOMILP) to determine the optimum order quantity of each supplier under uncertain conditions. To deal with the uncertain multi-objectiveness of the proposed model, a robust goal programming (RGP) approach based on Shannon entropy is applied. The offered methodology is applied to a real case study from a green service food manufacturing company in Iran in order to verify its applicability with a sensitivity analysis performed on different uncertainty levels. Furthermore, the threshold of robustness worthiness (TRW) is studied by applying different budgets of uncertainty for the green service food manufacturing company. Finally, a discussion and conclusion on the applicability of the methodology is provided, and an outlook to future research projects is given.

The purpose of this article was to demonstrate the difference between a pandemic plan’s textual prescription and its effective processing using graphical notation. Before creating a case study of the Business Process Model and Notation (BPMN) of the Czech Republic’s pandemic plan, we conducted a systematic review of the process approach in pandemic planning and a document analysis of relevant public documents. The authors emphasized the opacity of hundreds of pages of text records in an explanatory case study and demonstrated the effectiveness of the process approach in reengineering and improving the response to such a critical situation. A potential extension to the automation and involvement of SMART technologies or process optimization through process mining techniques is presented as a future research topic.

Waste collection is a highly visible municipal service that involves large expenditures and difficult operational problems. In addition, it is expensive to operate in terms of investment costs (i.e. vehicles fleet), operational costs (i.e. fuel and maintenances) so that generating small improvements in this area can lead to huge savings in municipal expenditures. Among the issues raised in the process of decisions making by managers and associated policy makers, one can point to determining the optimal weekly policies of waste collection. In this paper, the periodic capacitated arc routing problem (PCARP)in mobile disposal sites is described and the authors seek to determine the optimal routes of required edges (streets or alleys) per week, number and location of mobile disposal sites, and the number of required vehicles. We present two simulated annealing algorithms, which are different in cooling schedule and number of iterations of each temperature. To evaluate the performance of these algorithms on small-sized problems, the solver “CPLEX"in application “GAMS” is used. The experimental results show that the presented algorithms have appropriate performance and a reasonable time range.